A lot of players have had trouble getting the timing right to get the bird holding the missing puzzle piece to break the wire it's perched on. Forum member Plasmadog has discovered a sure-fire way:

"There is a small piston at the right of the screen, a little way behind the cat, going up and down. If you move the robot up and down roughly in sync with that piston, the wire should break. It worked for me within seconds of trying it, which seems to be the typical result."

I saw on YouTube on some Machinarium videos that people are "forcing" the wire to break up. The solution to break it "soft " is to easly move up and down your cursor accelerating every movement session. If it doesn't break , not even when you reached force movement, try it again from the lowest speed.

Sorry if I wrote some sentences wrong. I don't speak english at perfection

I just tried it now, the method that ABoretz posted didn't really work... but thanks anyway! I tried Raining Tip's method but went a bit different... I moved my cursor up & down to the top & bottom of the game screen quickly.